Question: Umaima is 6 years younger than Daniel. For the last four years, Daniel and Umaima have been going to the same school. Four years ago, Daniel was 4 times older than Umaima. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Umaima. Let Daniel's current age be $d$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $d = u + 6$ Four years ago, Daniel was $d - 4$ years old, and Umaima was $u - 4$ years old. The information in the second sentence can be expressed in the following equation: $d - 4 = 4(u - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = d - 6$ . Substituting this into our second equation, we get the equation: $d - 4 = 4($ $(d - 6)$ $ -$ $ 4)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 4 = 4d - 40$ Solving for $d$ , we get: $3 d = 36$ $d = 12$.